Tom B has rather extensively covered the case of a more efficient A-H.
I would mention another case that might quite likely change the whole outcome of WWI and subsequent European history. Namely, Italy taking the side of the Central Powers.
The PoD for this will be Germany successfully persuading A-H to give Italy some territorial compensations (at least Trento, Gorizia-Gradisca, and Trieste shall be necessary). OTL, these negotiations took place, but floundered (and Italy therefore went to the Entente) because A-H dragged their feet about giving up any of their ethnically-Italian territories.
If at least part of their long-standing irredentist claims vs. A-H shall be satisfied, Italy loses her main motivation not to be true to her old alliance committments. They also have significant irredentist and colonial claims vs. France, which Germany and A-H will be as generous to promise satisfaction about, as the Entente was vs. A-H OTL.
Thre are two likely windows for CP Italy to enter the war, either August-September 1914 or April-May 1915. Both are possible, but the latter is more probable since it may need the realization WWI is not going to be a short war, for Germany to become sufficiently determined to get Italy in the war and overcome A-H resistance.
Anyway, differently from WWII, Italy's Army and Navy in 1914-15 were of a comparable quality to the other Great Powers and her entry changes the strategic balance in favour of the CP considerably. The bluk of the Italian Army will attack on the Alps, which were much less fortified than the Dolomites in 1914-15. This will force the Anglo-French to redeploy at least 25-30% of their manpower on the Alps.
If this happens in 1914, it has good potential to overstretch the French Army critically and cause its collapse in the Battle of the Marne. Otherwise, or if negotiations to secure Italy delay her entry till Spring 1915, the Alps front will most likely stabilize after limited Italian advances, and a long string of mountain trench warfare and inconclusive offensives will follow, much similar to OTL, only on the other side of the Alps.
However, this will drain French manpower rather faster and more severely, even with British assistance it may easily become exausted in 1916-17, especially if the Germans and the Italians start to coordinate their offensives, so that Anglo-French strategic reserves cannot be used to plug local CP breakthroughs.
German-Italian strategic cooperation is quite reasonable, since Triple Alliance had standing military protocols to transfer leftover Italian manpower on the German front in case of war since the 1890s, which only need to be dusted off ITTL. This, too, will heighten the pressure on the French.
Another big favourable effect for the CPs from the Italian alliance will be that the full military potential of A-H, once Serbia is dealt with, can be used on the Russian front. Also the Germans and the Italians can transfer more of their forces on the Russian front. This will increase the severity and quickness of Russian casualties and accelerate the collapse of Russia.
The third, only slightly less important, effect is that the Italian, Turkish, and A-H Navies, in cooperation, can certainly give serious problems to the Entente in the Mediterranean. Moving colonial troops from French Africa to Europe becomes rather more problematic, and the British Navy will be forced to either give up the Mediterranean to a large extent, or weaken the North Sea Fleet.
The fourth effect, not so decisive, but still significant, is that Serbia shall collapse rather more quickly and even more decisively, since Italy will most likely land an expedition corps in Albania and Motenegro and backstab Serbia. This may cause her collapse in late 1914, or the complete destruction of the Serbian Army in 1915. There will be no Salonicco front, and the Ottomans can redeploy more of their forces in the Caucasus.
In sum, the most probable outcome of this alliance is the collapse of either France or, most likely, Russia in 1916. Germany will have no good reason to employ unrestricted submarine warfare, so no USA help for the Entente. The full combined manpower (minus whatever occupation armeis for the defeated Entente nation) of DE-AU-IT shall be redeployed on either Russia or, most likely, France in 1917 causing a strategic breakthrough, despite British help.